few_shots: Example:
Problem/activity:
Problem 1
The table below contains single equations in a single variable, single equations in two variables, and pairs of simultaneous equations in two variables. Check the appropriate box to show whether there is no solution, exactly 1 solution, or if there is an infinite number of solutions.
|                                                          | **           No solution          ** | **           Exactly 1 solution          ** | **           Infinite number of solutions          ** |
|----------------------------------------------------------|--------------------------------------|---------------------------------------------|-------------------------------------------------------|
|                       $${9=4x+7}$$                       |                                      |                                             |                                                       |
|                       $${y=3y+5}$$                       |                                      |                                             |                                                       |
|                    $${y={x\over2}}$$                     |                                      |                                             |                                                       |
|                     $${3x+6y-9=0}$$                      |                                      |                                             |                                                       |
|    $${x=y}$$                        $${1.25x=1.25y}$$    |                                      |                                             |                                                       |
| $${9.9=6x+8y}$$                        $${9x=2.5y-8.8}$$ |                                      |                                             |                                                       |
| $${11x-2y=1.5}$$                        $${11x-2y=2.5}$$ |                                      |                                             |                                                       |
Problem 2
Kim has a small container and a large container as shown.
[IMG]
It takes 16 of the small containers to fill the large container. Three small containers leave 1.95 gallons of space in the big container.
What is the size of each of the two containers?


Topic options: 
A. Modeling: students learn to choose and use appropriate mathematics and statistics to analyze real-world empirical situations, improve decisions, and report on their conclusions and the reasoning behind them.
B. Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.
C. Statistics & Probability: students learn to analyze and produce data distributions, and build understanding of univariate and bivariate data. They learn to interpret data, make statistical inferences, justify conclusions, understand rules of probability, and use probability to make decisions.
D. Geometry: students learn to classify geometric figures by their properties, and understand and compare the relationships between them. Students develop and use formulas to compute lengths, areas, and volumes, and they use transformations to generate new shapes and compare existing ones. Geometry can be studied with and without coordinates.
E. Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.
F. Operations & Algebra: students learn to solve problems using algebraic thinking and operations such as addition, subtraction, multiplication, and division. They may learn to identify and explain arithmetic patterns, evaluate or manipulate numerical expressions, and reason with equations and inequalities.
G. Functions: students learn to define, use, and evaluate functions to model relationships between quantities.
H. Measurement & Data: students learn to work with data and measure attributes such as time, money, length, area, and volume. They may learn to compare measurements to operations and convert between different units of measure.
I. Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.
J. Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.
K. Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.


Thought: This set of problems asks students to reason with equations, specifically linear equations, such as the one shown in the table in Problem 1.
Answer: F

Now, assign the following problem or activity to one or more relevant topics it teaches.
shot_info: fl_problem_001392

8
options: Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.

Operations & Algebra: students learn to solve problems using algebraic thinking and operations such as addition, subtraction, multiplication, and division. They may learn to identify and explain arithmetic patterns, evaluate or manipulate numerical expressions, and reason with equations and inequalities.

Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.

Statistics & Probability: students learn to analyze and produce data distributions, and build understanding of univariate and bivariate data. They learn to interpret data, make statistical inferences, justify conclusions, understand rules of probability, and use probability to make decisions.

Measurement & Data: students learn to work with data and measure attributes such as time, money, length, area, and volume. They may learn to compare measurements to operations and convert between different units of measure.

Geometry: students learn to classify geometric figures by their properties, and understand and compare the relationships between them. Students develop and use formulas to compute lengths, areas, and volumes, and they use transformations to generate new shapes and compare existing ones. Geometry can be studied with and without coordinates.

Functions: students learn to define, use, and evaluate functions to model relationships between quantities.

Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.

Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.

Modeling: students learn to choose and use appropriate mathematics and statistics to analyze real-world empirical situations, improve decisions, and report on their conclusions and the reasoning behind them.

Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.
problem_activity: Narrative
The purpose of this activity is for students to write equations for multiplication situations and diagrams using a symbol for the unknown number. When students write an equation to represent a situation, including a symbol for the unknown number, they model a situation with mathematics (MP4).
Students find an unknown factor or unknown product in multiplication problems. In this task, the unknown factor diagrams and situations only include the “how many groups” problem type and the factors 2, 5, and 10. This sets students up to skip-count to find the unknown number.
This problem type will be revisited extensively in future lessons and will be related to division. It is not necessary to make the connection to division now. In the synthesis students explain how the equations they wrote represent the diagram or situation.
Representation: Internalize Comprehension.
Synthesis: Invite students to identify which details were important or most useful to pay attention to. Display the sentence frame, “The next time I write an equation with an unknown number, I will . . . .“
Supports accessibility for: Visual-Spatial Processing
Launch
Groups of 2
Activity
“Now you will practice writing your own equations with a symbol for the unknown.”
2–3 minutes: independent work time
“Share your equations with your partner. Discuss how you know each equation matches the diagram or situation.”
2–3 minutes: partner discussion
Have a whole-class discussion focused on how the equations match the different representations.
Consider asking:
“How did you use the representations to write an equation with a symbol for the unknown?” (I looked for what was missing in the diagram. I thought about the situation to figure out if it was the number in each group, the number of groups, or the total that was missing.)
“Now find the missing number in each equation and write a new equation that includes the solution.”
3–5 minutes: partner work time
Student Facing
Write an equation to represent each diagram or situation. Use a symbol for the unknown. Be prepared to share your reasoning.
Find the number that makes each equation true. Rewrite the equation with the solution.
|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 diagram or situation                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 | equation with symbol | equation with solution |
|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|----------------------|------------------------|
| |https://cms-im.s3.amazonaws.com/gf3w2hjep7il38vg6usxrnj0zj9v?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-152934.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-152934.svg&response-content-type=image%2Fsvg%2Bxml&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240208%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240208T163829Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=e5ec58d09b006a5b2fe4be0a8c6e1be79921b2ef4899756a6a2fb56b666e8275|  |https://cms-im.s3.amazonaws.com/gf3w2hjep7il38vg6usxrnj0zj9v?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-152934.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-152934.svg&response-content-type=image%2Fsvg%2Bxml&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240208%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240208T163829Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=e5ec58d09b006a5b2fe4be0a8c6e1be79921b2ef4899756a6a2fb56b666e8275| image:: https://cms-im.s3.amazonaws.com/gf3w2hjep7il38vg6usxrnj0zj9v?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-152934.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-152934.svg&response-content-type=image%2Fsvg%2Bxml&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240208%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240208T163829Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=e5ec58d09b006a5b2fe4be0a8c6e1be79921b2ef4899756a6a2fb56b666e8275 |                      |                        |
|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               Jada has some packs of sports cards. Each pack has 5 cards. If Jada has 45 cards, how many packs of cards does she have?                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               |                      |                        |
| |https://cms-im.s3.amazonaws.com/clhjdxlivcrwuhnz8p74h3wdr0sr?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-148281.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-148281.svg&response-content-type=image%2Fsvg%2Bxml&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240208%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240208T163829Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=d838c3f51f69439465afa72015e1148ef93bd40389ba4d8f653044f160e7cc19|  |https://cms-im.s3.amazonaws.com/clhjdxlivcrwuhnz8p74h3wdr0sr?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-148281.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-148281.svg&response-content-type=image%2Fsvg%2Bxml&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240208%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240208T163829Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=d838c3f51f69439465afa72015e1148ef93bd40389ba4d8f653044f160e7cc19| image:: https://cms-im.s3.amazonaws.com/clhjdxlivcrwuhnz8p74h3wdr0sr?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-148281.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-148281.svg&response-content-type=image%2Fsvg%2Bxml&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240208%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240208T163829Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=d838c3f51f69439465afa72015e1148ef93bd40389ba4d8f653044f160e7cc19 |                      |                        |
| |https://cms-im.s3.amazonaws.com/jg4dxs24ozz1huvon7s4enxj1zdl?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-148282.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-148282.svg&response-content-type=image%2Fsvg%2Bxml&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240208%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240208T163829Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=8cf7dafc0a1b5a31eead8875981bb2db673480a12c4a842012b6e72effafc408|  |https://cms-im.s3.amazonaws.com/jg4dxs24ozz1huvon7s4enxj1zdl?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-148282.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-148282.svg&response-content-type=image%2Fsvg%2Bxml&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240208%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240208T163829Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=8cf7dafc0a1b5a31eead8875981bb2db673480a12c4a842012b6e72effafc408| image:: https://cms-im.s3.amazonaws.com/jg4dxs24ozz1huvon7s4enxj1zdl?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-148282.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-148282.svg&response-content-type=image%2Fsvg%2Bxml&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240208%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240208T163829Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=8cf7dafc0a1b5a31eead8875981bb2db673480a12c4a842012b6e72effafc408 |                      |                        |
|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         The school has 6 bags. Each bag has 10 basketballs in it. How many basketballs does the school have?                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         |                      |                        |
Student Response
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Advancing Student Thinking
If students write an equation without a symbol for the unknown number, consider asking:
“How does your equation represent the diagram (or situation)?”
“How could you show the number that was unknown with a symbol?”
Activity Synthesis
“What strategies did you use to find the unknown numbers?” (I counted by 2 to get the total. I counted by different numbers until I found a number that gave me the product.)
“How did each equation change as you found the unknown number?” (The symbol was replaced with the number.)


correct_option_index: 1